Despite a state government shutdown due to a snowfall, five Democrats vying for the nomination for governor in November faced off in a lively debate in the Globe Lab this afternoon, debating issues including education, transportation, and the best way to attract technology companies to Massachusetts.

The candidates tried to distinguish themselves on their approaches to leadership while agreeing on most policy matters. All five said they oppose the death penalty for accused Boston Marathon bomber Dzhokhar Tsarnaev, and all said that Governor Deval Patrick was right to order the lockdown in the wake of the Marathon bombings when the suspects remained at large. All five also embraced the new Common Core education standards, saying Massachusetts needs to adopt them to acquire federal funding.

The candidates also debated the crisis at the Department of Children and Families, which lost track of a 5-year-old Fitchburg boy reported missing in December and now feared dead.

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Martha Coakley called DCF a “tough topic for me,” noting that as Middlesex County district attorney, her office handled more than 900 cases of child abuse every year.

Pointing to the divergent pressures placed on case workers — to keep families together but keep them safe — she pointed to long-standing problems that will likely be resurfaced in an ongoing investigation into the lapse.

“Of course, we need more social workers who are better trained. I can tell you what that review will tell us. Everybody knows what that review will tell us,” Coakley said. She called for a “dedicated unit” that would handle serious cases and better track children.

Juliette Kayyem challenged the notion that the problems are already known. “Never underestimate government’s capacity to learn,” Kayyem said, noting that recommendations for long-term solutions might involve better training or more funding. “Part of our obligation to citizens who pay taxes ... is to say, we’re going to get better, too.”

Steve Grossman said the DCF situation points to a deeper question — whether reduced funding for social services has unreasonably increased the burden on case workers.

“This gets back to the fundamental issue. You judge a society by how we spend our resources. And we’re not spending enough on our children,” Grossman said.

Joe Avellone said families’ issues are often rooted in mental health and substance abuse, the treatment of which has suffered from budget cutbacks in recent years.

“We took what was already an underinvested system and whittled it back during the recession. This is an investment we have to make,” added Avellone.

Don Berwick said he would address the problem at DCF by running government “the way a great business runs — with an empowered workforce,” and by never accepting a failure when the outcome is the loss of a child.